The Tikka is a light weight rifle. I have one in 7mm-08 and love it. Shoots great, easy handling and is just great for going up and down trees. Recoil is not a issue, but I think it would be with a 7wsm. My gun is a ss/ synthetic and weighs 7 1/4 pounds, scoped, loaded and sling. Put that number in a recoil calculator = ouch.
If the 7wsm is it for you , I would consider the Sako with a little more weight. I think it will be more enjoyable to shoot, and you will shoot it better.
But who am I to say, just got a .338 win mag and have really enjoyed shooting it. Something about that 180 gran ballistic tip going 3300 fps that makes me say errrrrrrr!
Bubba Jack